United States
Department of
Agriculture
Forest Service
Forest Management
Service Center
Fort Collins, CO
2008
Southeast Alaska and Coastal
British Columbia (AK) Variant
Overview
Forest Vegetation Simulator
Revised:
March 30, 2016
Sitka Ranger District, AK
(Thomas Witherspoon, FS-R10)
ii
Southeast Alaska and Coastal British
Columbia (AK) Variant Overview
Forest Vegetation Simulator
Compiled By:
Chad E. Keyser
USDA Forest Service
Forest Management Service Center
2150 Centre Ave., Bldg A, Ste 341a
Fort Collins, CO 80526
Authors and Contributors:
The FVS staff has maintained model documentation for this variant in the form of a variant overview
since its release in 1985. The original authors were Gary Dixon, Ralph Johnson, and Dan Schroeder. In
2008, the previous document was replaced with this updated variant overview. Gary Dixon,
Christopher Dixon, Robert Havis, Chad Keyser, Stephanie Rebain, Erin Smith-Mateja, and Don
Vandendriesche were involved with this update. Erin Smith-Mateja cross-checked information
contained in this variant overview with the FVS source code. Current maintenance is provided by Chad
Keyser.
Keyser, Chad E. comp. 2008 (revised March 30, 2016). Southeast Alaska and Coastal British Columbia
(AK) Variant Overview – Forest Vegetation Simulator. Internal Rep. Fort Collins, CO: U. S. Department
of Agriculture, Forest Service, Forest Management Service Center. 40p.
iii
Table of Contents
1.0 Introduction................................................................................................................................ 1
2.0 Geographic Range ....................................................................................................................... 2
3.0 Control Variables ........................................................................................................................ 4
3.1 Location Codes ..................................................................................................................................................................4
3.2 Species Codes ....................................................................................................................................................................4
3.3 Habitat Type, Plant Association, and Ecological Unit Codes .............................................................................................5
3.4 Site Index ...........................................................................................................................................................................5
3.5 Maximum Density .............................................................................................................................................................6
4.0 Growth Relationships.................................................................................................................. 8
4.1 Height-Diameter Relationships .........................................................................................................................................8
4.2 Bark Ratio Relationships..................................................................................................................................................10
4.3 Crown Ratio Relationships ..............................................................................................................................................11
4.3.1 Crown Ratio Dubbing...............................................................................................................................................11
4.3.2 Crown Ratio Change ................................................................................................................................................13
4.3.3 Crown Ratio for Newly Established Trees ...............................................................................................................13
4.4 Crown Width Relationships .............................................................................................................................................14
4.5 Crown Competition Factor ..............................................................................................................................................15
4.6 Small Tree Growth Relationships ....................................................................................................................................16
4.6.1 Small Tree Height Growth .......................................................................................................................................16
4.6.2 Small Tree Diameter Growth ...................................................................................................................................18
4.7 Large Tree Growth Relationships ....................................................................................................................................18
4.7.1 Large Tree Diameter Growth ...................................................................................................................................19
4.7.2 Large Tree Height Growth .......................................................................................................................................22
5.0 Mortality Model ....................................................................................................................... 26
6.0 Regeneration ............................................................................................................................ 28
7.0 Volume ..................................................................................................................................... 30
8.0 Fire and Fuels Extension (FFE-FVS)............................................................................................. 32
9.0 Insect and Disease Extensions ................................................................................................... 33
10.0 Literature Cited ....................................................................................................................... 34
11.0 Appendices ............................................................................................................................. 37
11.1 Appendix A: Site Index Conversion Information ...........................................................................................................37
iv
Quick Guide to Default Settings
Parameter or Attribute
Default Setting
Number of Projection Cycles
1 (10 if using Suppose)
Projection Cycle Length
10 years
Location Code (National Forest)
1005 – Tongass National Forest: Ketchikan Area
Slope
5 percent
Aspect
0 (no meaningful aspect)
Elevation
10 (100 feet)
Latitude / Longitude
Latitude
Longitude
All location codes
56
132
Site Species
WH
Site Index
80 feet (breast height age; 50 years)
Maximum Stand Density Index
Species specific
Maximum Basal Area
Based on maximum stand density index
Volume Equations
National Volume Estimator Library
Merchantable Cubic Foot Volume Specifications:
Minimum DBH / Top Diameter
Hardwoods
Softwoods
All location codes
11.0 / 8.0 inches
9.0 / 6.0 inches
Stump Height
1.0 foot
1.0 foot
Merchantable Board Foot Volume Specifications:
Minimum DBH / Top Diameter
LP
All other species
All location codes
8.0 / 6.0 inches
9.0 / 6.0 inches
Stump Height
1.0 foot
1.0 foot
Sampling Design:
Basal Area Factor
62.5 BAF
Small-Tree Fixed Area Plot
1/300th Acre
Breakpoint DBH
5.0 inches
v
1.0 Introduction
The Forest Vegetation Simulator (FVS) is an individual tree, distance independent growth and yield
model with linkable modules called extensions, which simulate various insect and pathogen impacts,
fire effects, fuel loading, snag dynamics, and development of understory tree vegetation. FVS can
simulate a wide variety of forest types, stand structures, and pure or mixed species stands.
New “variants” of the FVS model are created by imbedding new tree growth, mortality, and volume
equations for a particular geographic area in the FVS framework. Geographic variants of FVS have been
developed for most of the forested lands in the United States.
In 1984, the Alaska Region, Forest Service, U.S. Department of Agriculture requested a variant be
developed for the western hemlock-Sitka spruce forest type in southeast Alaska. The Alaska Region,
Pacific Northwest Research Station, Forest Inventory and Analysis (Anchorage), and the British
Columbia Ministry of Forests decided to include all National Forest and Crown land falling in this
vegetative type regardless of state or country boundaries. This variant became known as the “AK”
variant, covering Southeast Alaska and Coastal British Columbia.
The AK variant is sometimes referred to as the “SEAPROG” variant, referring to the geographic area for
which it was calibrated (South East Alaska) and the model structure on which it was originally based
(PROGnosis) (Stage 1973).
Since the variant’s development in 1984, virtually all of the functions have been adjusted and improved
as more data has become available, and as model technology has improved.
To fully understand how to use this variant, users should also consult the following publication:
•
Essential FVS: A User’s Guide to the Forest Vegetation Simulator (Dixon 2002)
This publication can be downloaded from the Forest Management Service Center (FMSC), Forest
Service website or obtained in hard copy by contacting any FMSC FVS staff member. Other FVS
publications may be needed if one is using an extension that simulates the effects of fire, insects, or
diseases.
1
2.0 Geographic Range
The AK variant was fit to data representing southeast Alaska coastal forest types, namely the hemlockSitka spruce forest type. Data used in initial model development came from the Juneau forest
inventory, Stikine forest inventory, Sitka forest inventory, young growth stand exams (from throughout
the area), young growth surveys (questionnaires), growing stock studies (Bill Farr, PNW), Makah Indian
Reservation, Queen Charlotte Islands Forest Inventory, and Prince of Wales Forest Inventory.
Distribution of data samples for species fit from this data are shown in table 2.0.1.
Table 2.0.1 The distribution of original growth sample trees by species for the AK variant.
Species
white spruce
western redcedar
Pacific silver fir
mountain hemlock
western hemlock
Alaska cedar
lodgepole pine
Sitka spruce
subalpine fir
hardwoods
Total Number of Observations
0
402
98
908
5581
880
78
3017
1
69
The AK variant covers the southeast Alaska coastal forest types. This includes all or part of the
Chatham, Ketchikan, and Stikine areas of the Tongass National Forest, corresponding Industry lands,
coastal British Columbia, the Queen Charlotte Islands / Haida Gwaii, and the extreme northwestern tip
of the Olympic Peninsula. The AK variant was not fit to other forest types in Alaska, but it is currently
the best available variant for those areas. The suggested geographic range of use for the AK variant is
shown in figure 2.0.1.
2
Figure 2.0.1 Suggested geographic range of use for the AK variant.
3
3.0 Control Variables
FVS users need to specify certain variables used by the AK variant to control a simulation. These are
entered in parameter fields on various FVS keywords usually brought into the simulation through the
SUPPOSE interface data files or they are read from an auxiliary database using the Database Extension.
3.1 Location Codes
The location code is a 3- or 4-digit code where, in general, the first two digits of the code represents
the Forest Service Alaska Region Number, and the last two digits represent the Forest
Number/management area within that region. In some cases, a location code beginning with a “7” or
“8” is used to indicate an administrative boundary that doesn’t use a Forest Service Region number (for
example, Indian Reservations, Industry Lands, or other lands).
If the location code is missing or incorrect in the AK variant, a default forest code of 1005 (Tongass
National Forest: Ketchikan Area) will be used. A complete list of location codes recognized in the AK
variant is shown in table 3.1.1.
Table 3.1.1 Location codes used in the AK variant.
Location Code
701
1002
1003
1004
1005
Location
British Columbia / Makah Indian Reservation
Tongass National Forest: Stikine Area
Tongass National Forest: Chatham Area
Chugach National Forest
Tongass National Forest: Ketchikan Area
3.2 Species Codes
The AK variant recognizes 13 species. You may use FVS species alpha codes, Forest Inventory and
Analysis (FIA) species codes, or USDA Natural Resources Conservation Service PLANTS symbols to
represent these species in FVS input data. Any valid western species codes identifying species not
recognized by the variant will be mapped to the most similar species in the variant. The species
mapping crosswalk is available on the variant documentation webpage of the FVS website. Any nonvalid species code will default to the “other softwoods” category.
Either the FVS sequence number or alpha code must be used to specify a species in FVS keywords and
Event Monitor functions. FIA codes or PLANTS symbols are only recognized during data input, and may
not be used in FVS keywords. Table 3.2.1 shows the complete list of species codes recognized by the
AK variant.
Table 3.2.1 Species codes used in the AK variant.
Species
Number
1
2
Species
Code
WS
RC
Common Name
white spruce
western redcedar
FIA
Code
094
242
4
PLANTS
Symbol
PIGL
THPL
Scientific Name
Picea glauca
Thuja plicata
Species
Number
3
4
5
6
7
8
9
10
11
12
13
Species
Code
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
OS
Common Name
Pacific silver fir
mountain hemlock
western hemlock
Alaska cedar
lodgepole pine
Sitka spruce
subalpine fir
red alder
black cottonwood
other hardwoods
other softwoods
FIA
Code
011
264
263
042
108
098
019
351
747
998
298
PLANTS
Symbol
ABAM
TSME
TSHE
CANO9
PICO
PISI
ABLA
ALRU2
POBAT
2TD
2TE
Scientific Name
Abies amabilis
Tsuga mertensiana
Tsuga heterophylla
Callitropsis nootkatensis
Pinus contorta
Picea sitchensis
Abies lasiocarpa
Alnus rubra
Populus trichocarpa
3.3 Habitat Type, Plant Association, and Ecological Unit Codes
Habitat type, plant association, and ecological unit codes are not used in the AK variant.
3.4 Site Index
Site index is used in the AK variant and is an input variable for some of the growth equations. Farr
(1984) western hemlock and Sitka spruce (50 year base; breast height age) equations are the FVS
referenced equations for site index. Site index taken using a site curve other than Farr (1984) for
western hemlock or Sitka spruce, will need to be converted to one of these two referenced curves.
Users can enter site index values for any, or all, species. FVS will estimate site index values using the
site index of the designated site species for any species for which the users do not provide a value as
shown in table 3.4.1.
Table 3.4.1 Site Index Conversions for all species in the AK variant.
Species
Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
Conversion from Farr's
WH to another species
= SI(WH)
= SI(WH)
= SI(WH)
= SI(WH)
= SI(WH)
= SI(WH)
= -28.97 + 1.187*SI(WH)
= -6.62+1.152*SI(WH)
= -28.97 + 1.187*SI(WH)
= -5.8812+0.5294*SI(WH)
= 18.3112+1.2692*SI(WH)
= SI(WH)
Conversion from Farr's SS
to another species
= 24.41+0.674*SI(SS)
= 24.41+0.674*SI(SS)
= 24.41+0.674*SI(SS)
= 24.41+0.674*SI(SS)
= 24.41+0.674*SI(SS)
= 24.41+0.674*SI(SS)
= 0.8*SI(SS)
= SI(SS)
= 0.8 * SI(SS)
= 7.0388 + 0.3568*SI(SS)
= 49.2797 + 0.8554*SI(SS)
= 24.41+0.674*SI(SS)
5
Species
Code
OS
Conversion from Farr's
WH to another species
= SI(WH)
Conversion from Farr's SS
to another species
= 24.41+0.674*SI(SS)
Data sets used to build the AK variant came from a variety of sources that referenced different site
quality techniques. These sources included Hegyi et al (1981) site curves, Stephen et al (1969) site
curves, Taylor (1934) site curves, Farr (1984) site curves, and soil series data for southeast Alaska and
British Columbia. Information on how these curves were originally converted to Farr (1984) site index
values can be found in Appendix A.
3.5 Maximum Density
Maximum stand density index (SDI) and maximum basal area (BA) are important variables in
determining density related mortality and crown ratio change. Maximum basal area is a stand level
metric that can be set using the BAMAX or SETSITE keywords. If not set by the user, a default value is
calculated from maximum stand SDI each projection cycle. Maximum stand density index can be set for
each species using the SDIMAX or SETSITE keywords. If not set by the user, a default value is assigned
as discussed below. Maximum stand density index at the stand level is a weighted average, by basal
area proportion, of the individual species SDI maximums.
The default maximum SDI is set by species or a user specified basal area maximum. If a user specified
basal area maximum is present, the maximum SDI for all species is computed using equation {3.5.1};
otherwise, species SDI maximums are assigned from the SDI maximums shown in table 3.5.1.
{3.5.1} SDIMAXi = BAMAX / (0.5454154 * SDIU)
where:
SDIMAXi
BAMAX
SDIU
is the species-specific SDI maximum
is the user-specified stand basal area maximum
is the proportion of theoretical maximum density at which the stand reaches actual
maximum density (default 0.85, changed with the SDIMAX keyword)
Table 3.5.1 Stand density index maximums by species in the AK variant.
Species Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
SDI Maximum
750
750
750
750
750
750
750
750
750
750
750
6
Species Code
OH
OS
SDI Maximum
750
750
7
4.0 Growth Relationships
This chapter describes the functional relationships used to fill in missing tree data and calculate
incremental growth. In FVS, trees are grown in either the small tree sub-model or the large tree submodel depending on the diameter.
4.1 Height-Diameter Relationships
Height-diameter relationships in FVS are primarily used to estimate tree heights missing in input data,
and occasionally to estimate diameter growth on trees smaller than a given threshold diameter. For
white spruce, western redcedar, Pacific silver fir, mountain hemlock, Alaska cedar, lodgepole pine,
subalpine fir, other hardwoods and other softwoods in the AK variant, height-diameter relationships
are a logistic functional form as shown in equation {4.1.1} (Wykoff, et.al 1982). Coefficients for the
equation are shown in tables 4.1.1 and 4.1.2 by crown ratio class values. Red alder and black
cottonwood use equation {4.1.1} for trees greater than or equal to 5 inches DBH and equation {4.1.2}
for trees less than 5 inches DBH when calibration of the height-diameter function is turned on.
Western hemlock and Sitka spruce use equation {4.1.1} when the height prediction from Johnson’s SBB
Distribution is less than or equal to 0.
{4.1.1} HT = 4.5 + exp(B1 + B2 / (DBH + 1.0))
{4.1.2} HT = 0.0994 +4.9767*DBH
where:
HT
DBH
B1 - B2
is tree height
is tree diameter at breast height
are species-specific coefficients determined by crown ratio class shown in tables 4.1.1
and 4.1.2, respectively
When heights are given in the input data for 3 or more trees of a given species, the value of B1 in
equation {4.1.1} for that species is recalculated from the input data and replaces the default value
shown in table 4.1.1. In the event that the calculated value is less than zero, the default is used. For red
alder and black cottonwood, this calibration process is turned off by default and FVS will not
automatically use equation {4.1.1} even if you have enough height values in the input data. To override
this default, the user must use the NOHTDREG keyword and change field 2 to a 1.
Table 4.1.1 Default B1 coefficients for the logistic Wykoff equation {4.1.1} in the AK variant.
Species
Code
WS
RC
SF
MH
WH
YC
Crown Ratio Class
4
5
6
1
2
3
7
8
9
4.8945
4.8945
4.8945
4.9727
4.9727
4.9727
4.8753
4.8753
4.8753
4.606
4.606
4.606
4.606
4.606
4.606
4.606
4.606
4.606
4.8945
4.8945
4.8945
4.7407
4.7407
4.7407
4.9727
4.9727
4.9727
4.8753
4.8753
4.8753
4.7666
4.7666
4.7666
4.7666
4.7666
4.7666
4.8933
4.8933
4.8933
4.9013
4.9013
4.9013
4.8043
4.8043
4.8043
4.8028
4.8028
4.8028
4.8028
4.8028
4.8028
4.8028
4.8028
4.8028
8
Species
Code
LP
SS
AF
RA
CW
OH
OS
Crown Ratio Class
4
5
6
1
2
3
7
8
9
4.615
4.615
4.615
4.615
4.615
4.615
4.615
4.615
4.615
4.8945
4.8945
4.8945
4.9727
4.9727
4.9727
4.8753
4.8753
4.8753
4.8945
4.8945
4.8945
4.9727
4.9727
4.9727
4.8753
4.8753
4.8753
4.875
4.875
5.152
5.152
4.875
4.875
4.875
4.875
4.875
4.875
4.875
5.152
5.152
5.152
5.152
5.152
5.152
5.152
4.8028
4.8028
4.8028
4.8028
4.8028
4.8028
4.8028
4.8028
4.8028
4.8945
4.8945
4.8945
4.9727
4.9727
4.9727
4.8753
4.8753
4.8753
Table 4.1.2 B2 coefficients for the logistic Wykoff equation {4.1.1} in the AK variant.
Species
Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
OS
Crown Ratio Class
4
5
6
1
2
3
-6.8703
-6.8703
-6.8703
-8.9697
-8.9697
-7.6276
-7.6276
-7.6276
-7.6276
-7.6276
7
8
9
-8.9697
-10.4921
-10.4921
-10.4921
-7.6276
-7.6276
-7.6276
-7.6276
-6.8703
-6.8703
-6.8703
-8.9697
-8.9697
-8.9697
-10.4921
-10.4921
-10.4921
-12.0745
-12.0745
-12.0745
-11.8502
-11.8502
-11.8502
-11.8502
-11.8502
-11.8502
-8.7008
-8.7008
-8.7008
-8.9024
-8.9024
-8.9024
-9.4649
-9.4649
-9.4649
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-10.4718
-10.4718
-10.4718
-10.4718
-10.4718
-10.4718
-10.4718
-10.4718
-10.4718
-6.8703
-6.8703
-6.8703
-8.9697
-8.9697
-8.9697
-10.4921
-10.4921
-10.4921
-6.8703
-6.8703
-6.8703
-8.9697
-8.9697
-8.9697
-10.4921
-10.4921
-10.4921
-8.639
-8.639
-8.639
-8.639
-8.639
-8.639
-8.639
-8.639
-8.639
-13.576
-13.576
-13.576
-13.576
-13.576
-13.576
-13.576
-13.576
-13.576
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-11.2306
-6.8703
-6.8703
-6.8703
-8.9697
-8.9697
-8.9697
-10.4921
-10.4921
-10.4921
By default, red alder and black cottonwood in the AK variant will use the Curtis-Arney functional form
as shown in equation {4.1.3} to compute height (Curtis 1967, Arney 1985). Coefficients for these
equations are shown in table 4.1.3.
{4.1.3} Curtis-Arney functional form
DBH > 3.0”: HT = 4.5 + P2 * exp[-P3 * DBH ^ P4 ]
DBH < 3.0”: HT = [(4.5 + P2 * exp[-P3 * 3.0 ^ P4 ] – 4.51) * (DBH – 0.3) / 2.7] + 4.51
where:
HT
DBH
P2 - P4
is tree height
is tree diameter at breast height
are species and location specific coefficients shown in table 4.1.3
9
Table 4.1.3 Red alder (RA) and black cottonwood (CW) coefficients used in height-diameter
equations {4.1.3} and {4.1.4} in the AK variant.
Species
Code
P2
P3
P4
RA
139.4551
4.6989
-0.7682
CW
178.6441
4.5852
-0.6746
Western hemlock and Sitka spruce use equations {4.1.5} and {4.1.6} to compute height. Coefficients for
this equation are shown in table 4.1.4.
{4.1.5} PSI = C8 *((DBH-0.1)/(0.1+C1 -DBH))^C9
{4.1.6} HT= ((PSI/(1.0+PSI))*C2 +4.5
where:
PSI
DBH
HT
C8, C1, C9, C2
is an intermediate variable
is tree diameter at breast height
is tree height
are coefficients based on species shown in table 4.1.4
Table 4.1.4 Western hemlock and Sitka spruce coefficients used in height-diameter equations {4.1.5}
and {4.1.6} in the AK variant.
Species
Code
C8
WH
1.67853
SS
1.27598
C1
70
70
C9
0.95008
0.91893
C2
200
220
4.2 Bark Ratio Relationships
Bark ratio estimates are used to convert between diameter outside bark and diameter inside bark in
various parts of the model. In the AK variant, all species except red alder and black cottonwood use
equation {4.2.1} to calculate bark ratio. Red alder and black cottonwood use equation {4.2.2} to
calculate bark ratio.
{4.2.1} BRATIO = (DBH – DBT) / DBH
{4.2.2} BRATIO = (0.075256 + (0.94373 * DBH)) / DBH
where:
BRATIO
DBH
DBT
is species-specific bark ratio
is tree diameter at breast height
is double bark thickness (DBT = 0.186 * DBH^0.45417)
10
4.3 Crown Ratio Relationships
Crown ratio equations are used for three purposes in FVS: (1) to estimate tree crown ratios missing
from the input data for both live and dead trees; (2) to estimate change in crown ratio from cycle to
cycle for live trees; and (3) to estimate initial crown ratios for regenerating trees established during a
simulation.
4.3.1 Crown Ratio Dubbing
In the AK variant, crown ratios missing in the input data are predicted using different equations
depending on tree species and size. Live red alder and black cottonwood trees less than 1.0” in
diameter and dead trees of all species and sizes use equation {4.3.1.1} and one of the equations listed
below, {4.3.1.2} - {4.3.1.3}, to compute crown ratio. Red alder and black cottonwood use equations
{4.3.1.1} and {4.3.1.3}, where all other dead trees use equations {4.3.1.1} and {4.3.1.2}. Equation
coefficients are found in table 4.3.1.1.
{4.3.1.1} X = R1 + R2 * DBH + R3 * HT + R4 * BA + R5 * PCCF + R6 * HTAvg/HT + R7 * HTAvg + R8 * BA *
PCCF + R9 * MAI + N(0,SD)
{4.3.1.2} CR = 1 / (1 + exp(X))
{4.3.1.3} CR = ((X - 1) * 10 + 1) / 100
where:
CR
DBH
HT
BA
PCCF
HTAvg
MAI
N(0,SD)
R1 – R9
is crown ratio expressed as a proportion (bounded to 0.05 < CR < 0.95)
is tree diameter at breast height
is tree height
is total stand basal area
is crown competition factor on the inventory point where the tree is established
is average height of the 40 largest diameter trees in the stand
is stand mean annual increment
is a random increment from normal distribution with mean 0 and standard deviation of SD
are species-specific coefficients shown in table 4.3.1.1
Table 4.3.1.1 Coefficients for the crown ratio equation {4.3.1.1} in the AK variant.
Coefficient
R1
R2
R3
R4
R5
R6
R7
R8
R9
WS, RC
-1.66949
-0.209765
0
0.003359
0.011032
0
0.017727
-0.000053
0.014098
SF, MH,
WH, SS, AF
-0.426688
-0.093105
0.022409
0.002633
0
-0.045532
0
0.000022
-0.013115
Species Code
YC
-0.426688
-0.093105
0.022409
0.002633
0
-0.045532
0
0.000022
-0.013115
LP
-1.66949
-0.209765
0
0.003359
0.011032
0
0.017727
-0.000053
0.014098
11
RA, CW
5
0
0
0
0
0
0
0
0
OH
-1.66949
-0.209765
0
0.003359
0.011032
0
0.017727
-0.000053
0.014098
OS
-2.19723
0
0
0
0
0
0
0
0
Coefficient
SD
WS, RC
0.5
SF, MH,
WH, SS, AF
0.6957
Species Code
YC
0.931
LP
0.6124
RA, CW
0.5
OH
0.4942
OS
0.2
A Weibull-based crown model developed by Dixon (1985) as described in Dixon (2002) is used to
predict crown ratio for all live trees 1.0” in diameter or larger. To estimate crown ratio using this
methodology, the average stand crown ratio is estimated from stand density index using equation
{4.3.1.4}. Weibull parameters are then estimated from the average stand crown ratio using equations
in equation set {4.3.1.5}. Individual tree crown ratio is then set from the Weibull distribution, equation
{4.3.1.6} based on a tree’s relative position in the diameter distribution and multiplied by a scale
factor, shown in either equation {4.3.1.7} or {4.3.0.8}, which accounts for stand density. Crowns
estimated from the Weibull distribution are bounded to be between the 5 and 95 percentile points of
the specified Weibull distribution. Equation coefficients for each species for these equations are shown
in table 4.3.1.2.
{4.3.1.3} ACR = d0 + d1 * (SDIstand / SDImax ) * 100.0
{4.3.1.4} Weibull parameters A, B, and C are estimated from average crown ratio
A = a0
B = b0 + b1 * ACR
(B > 3 for RA and CW; B > 1 for all other species)
C = c0 + c1 * ACR (C > 2)
{4.3.1.5} Y = 1-exp(-((X-A)/B)^C)
{4.3.1.6} Used for red alder (RA) and black cottonwood (CW)
SCALE = 1 – 0.00167 * (CCF – 100)
{4.3.1.7} Used for all other species
SCALE = 1.5 – RELSDI
where:
ACR
SDIstand
SDImax
A, B, C
X
Y
is predicted average stand crown ratio for the species
is stand density index of the stand
is maximum stand density index
are parameters of the Weibull crown ratio distribution
is a tree’s crown ratio expressed as a percent / 10
is a trees rank in the diameter distribution (1 = smallest; ITRN = largest)
divided by the total number of trees (ITRN) multiplied by SCALE
SCALE
is a density dependent scaling factor (bounded to 0.3 < SCALE < 1.0)
CCF
is stand crown competition factor
RELSDI
is the relative site density index (Stand SDI / Maximum SDI)
a0 , b0-1 , c0-1 , and d0-1 are species-specific coefficients shown in table 4.3.2
12
Table 4.3.1.2 Coefficients for the Weibull parameter equations {4.3.1.3} and {4.3.1.4} in the AK
variant.
Species
Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
OS
a0
0
0
0
0
0
0
0
0
0
0
0
0
0
b0
0.15716
0.09466
0.15716
-0.0154
0.51379
0.2589
0.09499
0.15716
0.15716
0.035786
-0.238295
0.2589
0.15716
Model Coefficients
b1
c0
c1
d0
1.08293
0.82252 0.51383 5.75349
1.09576
3.042
0
4.54
1.08293
0.82252 0.51383 5.75349
1.12736
2.737
0
5.13162
1.0049
-3.13907 1.36446 6.09225
1.06314
-0.01906 0.58428 5.66144
1.10021
2.477
0
5.92905
1.08293
0.82252 0.51383 5.75349
1.08293
0.82252 0.51383 5.75349
1.121389
2.0408
0
4.656659
1.180163 3.044134
0
4.625125
1.06314
-0.01906 0.58428 5.66144
1.08293
0.82252 0.51383 5.75349
d1
-0.02508
0
-0.02508
-0.01422
-0.02772
-0.02779
-0.05757
-0.02508
-0.02508
-0.022612
-0.016042
-0.02779
-0.02508
4.3.2 Crown Ratio Change
Crown ratio change is estimated after growth, mortality and regeneration are estimated during a
projection cycle. Crown ratio change is the difference between the crown ratio at the beginning of the
cycle and the predicted crown ratio at the end of the cycle. Crown ratio predicted at the end of the
projection cycle is estimated for live tree records using the Weibull distribution, equations {4.3.1.3}{4.3.1.7}, for all species. Crown change is checked to make sure it doesn’t exceed the change possible if
all height growth produces new crown. Crown change is further bounded to 1% per year for the length
of the cycle to avoid drastic changes in crown ratio. Equations {4.3.1.1} – {4.3.1.3} are not used when
estimating crown ratio change.
4.3.3 Crown Ratio for Newly Established Trees
Crown ratios for newly established trees during regeneration are estimated using equation {4.3.3.1}. A
random component is added in equation {4.3.3.1} to ensure that not all newly established trees are
assigned exactly the same crown ratio.
{4.3.3.1} CR = 0.89722 – 0.0000461 * PCCF + RAN
where:
CR
PCCF
RAN
is crown ratio expressed as a proportion (bounded to 0.2 < CR < 0.9)
is crown competition factor on the inventory point where the tree is established
is a small random component
13
4.4 Crown Width Relationships
The AK variant calculates the maximum crown width for each individual tree based on individual tree
and stand attributes. Crown width for each tree is reported in the tree list output table and used for
percent cover (PCC) calculations in the model.
Crown width is calculated using equations {4.4.1} – {4.4.3}, and coefficients for these equations are
shown in table 4.4.1. The minimum diameter and bounds for certain data values are given in table
4.4.2. Equation numbers in table 4.4.1 are given with the first three digits representing the FIA species
code, and the last two digits representing the equation source.
{4.4.1} Crookston (2003); Equation 03
DBH > MinD: CW = [a1 * exp[a2 + (a3 * ln(CL)) + (a4 * ln(DBH)) + (a5 * ln(HT)) + (a6 * ln(BA))]]
DBH < MinD: CW = [a1 * exp[a2 + (a3 * ln(CL)) + (a4 * ln(MinD)) + (a5 * ln(HT)) + (a6 * ln(BA))]] * (DBH
/ MinD)
{4.4.2} Crookston (2005); Equation 05
DBH > MinD: CW = (a1 * BF) * DBH^a2 * HT^a3 * CL^a4 * (BA + 1.0)^a5 * (exp(EL) )^a6
DBH < MinD: CW = [(a1 * BF) * MinD^a2 * HT^a3 * CL^a4 * (BA + 1.0)^a5 * (exp(EL ))^a6 ] * (DBH /
MinD)
{4.4.3} Donnelly (1996); Equation 06
DBH > MinD: CW = a1 * DBH^a2
DBH < MinD: CW = [a1 * MinD^a2 ] * (DBH / MinD)
where:
BF
CW
CL
DBH
HT
BA
EL
MinD
a1 – a6
is a species-specific coefficient based on forest code (BF = 1.0 in the AK variant)
is tree maximum crown width
is tree crown length
is tree diameter at breast height
is tree height
is total stand basal area
is stand elevation in hundreds of feet
is the minimum diameter
are species-specific coefficients shown in table 4.4.1
Table 4.4.1 Coefficients for crown width equations {4.4.1} – {4.4.3} in the AK variant.
Species
Code
WS
RC
SF
MH
WH
YC
Equation
Number*
09305
24205
01105
26403
26305
04205
a1
6.7575
6.2382
4.4799
6.90396
6.0384
3.3756
a2
0.55048
0.29517
0.45976
0.55645
0.51581
0.45445
a3
-0.25204
-0.10673
-0.10425
-0.28509
-0.21349
-0.11523
14
a4
0.19002
0.23219
0.11866
0.20430
0.17468
0.22547
a5
0
0.05341
0.06762
0
0.06143
0.08756
a6
-0.00313
-0.00787
-0.00715
0
-0.00571
-0.00894
Species Equation
Code Number*
a1
a2
a3
a4
a5
a6
LP
10805
6.6941 0.81980 -0.36992 0.17722 -0.01202
-0.00882
SS
09805
8.48
0.70692 -0.38812 0.17127
0
0
AF
01905
5.8827 0.51479 -0.21501 0.17916 0.03277
-0.00828
RA
35106
7.0806
0.4771
0
0
0
0
CW
74705
4.4327 0.41505 -0.23264 0.41477
0
0
OH
74705
4.4327 0.41505 -0.23264 0.41477
0
0
OS
09305
6.7575 0.55048 -0.25204 0.19002
0
-0.00313
*Equation number is a combination of the species FIA code (###) and source (##).
Table 4.4.2 MinD values and data bounds for equations {4.4.1}-{4.4.3} in the AK variant.
Species
Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
OS
Equation
Number*
09305
24205
01105
26403
26305
04205
10805
09805
01905
35106
74705
74705
09305
MinD
1.0
1.0
1.0
n/a
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
EL min
1
1
4
n/a
1
16
1
n/a
10
n/a
n/a
n/a
1
EL max
85
72
72
n/a
72
62
79
n/a
85
n/a
n/a
n/a
85
CW
max
40
45
33
45
54
59
40
50
30
35
56
56
40
4.5 Crown Competition Factor
The AK variant uses crown competition factor (CCF) as a predictor variable in some growth
relationships. Crown competition factor (Krajicek and others 1961) is a relative measurement of stand
density that is based on tree diameters. Individual tree CCFt values estimate the percentage of an acre
that would be covered by the tree’s crown if the tree were open-grown. Stand CCF is the summation of
individual tree (CCFt) values. A stand CCF value of 100 theoretically indicates that tree crowns will just
touch in an unthinned, evenly spaced stand. Crown competition factor for an individual tree is
calculated using equation {4.5.1} for most species, while equation {4.5.2} is used for red alder and black
cottonwood. If diameter is less than 0.1”, the equation for all species is used to reset CCF for all
species. All species coefficients are shown in table 4.5.1.
{4.5.1} All species
DBH > 0.1”: CCFt = R1 + (R2 * DBH^0.87) + (R3 * DBH^1.74)
DBH < 0.1”: CCFt = 0.001
15
{4.5.2} Red alder and black cottonwood
0.1 <DBH < 1.0”: CCFt = (R1 + R2 + R3 ) * DBH
DBH > 1.0”: CCFt = R1 + (R2 * DBH) + (R3 * DBH^2)
where:
CCFt
DBH
R1 – R3
is crown competition factor for an individual tree
is tree diameter at breast height
are species-specific coefficients shown in table 4.5.1
Table 4.5.1 Coefficients for the CCF equations {4.5.1} – {4.5.2} in the AK variant.
Species
Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
OS
Model Coefficients
R1
R2
R3
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
0.115396
0.0441381
0.0042207
0.000450757 0.0029209 0.00473186
0.02987
0.02928
0.00717
0.02987
0.02928
0.00717
4.6 Small Tree Growth Relationships
Trees are considered “small trees” for FVS modeling purposes when they are smaller than some
threshold diameter. The threshold diameter is set to 3.0” for all species in the AK variant.
The small tree model is height-growth driven, meaning height growth is estimated first and diameter
growth is estimated from height growth. These relationships are discussed in the following sections.
4.6.1 Small Tree Height Growth
The small-tree height growth model predicts 10-year height increment for small trees based on site
index, crown ratio, and basal area. Height increment is then adjusted for cycle length. Potential height
growth for all species except red alder and black cottonwood is estimated using equation {4.6.1.1}.
Height growth for red alder and black cottonwood is estimated using equation {4.6.1.2}.
{4.6.1.1} Used for all species except red alder and black cottonwood
POTHTG = -4.0166 + 0.451 * CR - 0.00611 * BAL + 0.09426 * SI
{4.6.1.2} Used for red alder and black cottonwood
16
POTHTG = 10.20 – (0.03 * PCCF)
where:
POTHTG
CR
BAL
SI
PCCF
is potential height growth in ten-year interval
is a tree’s live crown ratio (compacted) expressed as a proportion
is total basal area in trees larger than the subject tree
is species site index (bounded to SI > 40)
is crown competition factor on the inventory point where the tree is established
For all species, a small random error is then added to the height growth estimate. The estimated height
growth is then adjusted to account for cycle length, user defined small-tree height growth
adjustments, and adjustments due to small tree height increment calibration from input data.
Height growth estimates from the small-tree model are weighted with the height growth estimates
from the large tree model over a range of diameters (Xmin and Xmax) in order to smooth the transition
between the two models. For example, the closer a tree’s DBH value is to the minimum diameter
(Xmin), the more the growth estimate will be weighted towards the small-tree growth model. The closer
a tree’s DBH value is to the maximum diameter (Xmax), the more the growth estimate will be weighted
towards the large-tree growth model. If a tree’s DBH value falls outside of the range given by Xmin and
Xmax, then the model will use only the small-tree or large-tree growth model in the growth estimate.
The weight applied to the growth estimate is calculated using equation {4.6.1.3}, and applied as shown
in equation {4.6.1.4}. The range of diameters for each species is shown in table 4.6.1.2.
{4.6.1.3}
DBH < Xmin : XWT = 0
Xmin < DBH < Xmax : XWT = (DBH - Xmin ) / (Xmax - Xmin )
DBH > Xmax : XWT = 1
{4.6.1.4} Estimated growth = [(1 - XWT) * STGE] + [XWT * LTGE]
where:
XWT
DBH
Xmax
Xmin
STGE
LTGE
is the weight applied to the growth estimates
is tree diameter at breast height
is the maximum DBH is the diameter range
is the minimum DBH in the diameter range
is the growth estimate obtained using the small-tree growth model
is the growth estimate obtained using the large-tree growth model
Table 4.6.1.2 Diameter bounds by species in the AK variant.
Species
Code
WS
RC
SF
MH
WH
Xmin
Xmax
2.0
2.0
2.0
2.0
2.0
5.0
5.0
5.0
5.0
5.0
17
Species
Code
YC
LP
SS
AF
RA
CW
OH
OS
Xmin
Xmax
2.0
2.0
2.0
2.0
3.0
3.0
2.0
2.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
4.6.2 Small Tree Diameter Growth
As stated previously, for trees being projected with the small tree equations, height growth is
predicted first, and then diameter growth. So both height at the beginning of the cycle and height at
the end of the cycle are known when predicting diameter growth. In the AK variant, diameter is
estimated using equation {4.6.2.1} for all species except Sitka spruce, red alder, and black cottonwood.
Sitka spruce uses equation {4.6.2.2}. Red alder and black cottonwood use the equation set {4.6.2.3}.
Diameter growth is found by subtracting the diameter at the beginning of the projection cycle from
that at the end of cycle while adjusting for bark thickness.
{4.6.2.1} Used for all species except Sitka spruce, red alder, and black cottonwood
DBH = (-6.39362/(Ln(HT-4.5)-4.2976))-1.0
{4.6.2.2} Used for Sitka spruce
DBH = (-5.09974/(Ln(HT-4.5)-4.21391))-1.0
{4.6.2.3} Used for red alder and black cottonwood
If calibration occurs: DBH= 3.102 + 0.021*HT
If calibration does not occur and HT > HAT3: DBH = exp(Ln((Ln(HT-4.5)-Ln(P2 ))/(-1.*P3 )) * 1./P4 )
If calibration does not occur and HT < HAT3HT > HAT3: DBH = (((HT-4.51)*2.7)/(4.5+P2 *exp(1.*P3 *(3.^P4 ))-4.51))+0.3
where:
DBH
HT
HAT3
P2 - P4
is tree diameter at breast height
is tree height
is tree height of a tree with a 3” DBH. HAT3 = 4.5 + P2 * exp((-1.*P3 *3.0^P4 ))
are species and location specific coefficients shown in table 4.1.3
4.7 Large Tree Growth Relationships
Trees are considered “large trees” for FVS modeling purposes when they are equal to, or larger than,
some threshold diameter. This threshold diameter is set to 3.0” for all species in the AK variant.
The large-tree model is driven by diameter growth meaning diameter growth is estimated first, and
then height growth is estimated from diameter growth and other variables. These relationships are
discussed in the following sections.
18
4.7.1 Large Tree Diameter Growth
The large tree diameter growth model used in most FVS variants is described in section 7.2.1 in Dixon
(2002). For most variants, instead of predicting diameter increment directly, the natural log of the
periodic change in squared inside-bark diameter (ln(DDS)) is predicted (Dixon 2002; Wykoff 1990;
Stage 1973; and Cole and Stage 1972). For variants predicting diameter increment directly, diameter
increment is converted to the DDS scale to keep the FVS system consistent across all variants.
The AK variant uses two different equations to predict large-tree diameter growth for all species
except red alder. Equation {4.7.1.1} is used to predict diameter growth for Sitka spruce and western
hemlock greater than or equal to 7.0” DBH, and trees of all sizes for all other species except red alder.
Coefficients for this equation are shown in tables 4.7.1.1 – 4.7.1.3. For western hemlock and Sitka
spruce equation {4.7.1.2} predicts diameter growth for trees with a DBH less than 10.0”. Coefficients
for this equation are given in tables 4.7.1.4 – 4.7.1.5. The two diameter growth estimates for western
hemlock and Sitka spruce are weighted together for trees between 7” and 10” DBH. The “other
hardwoods” species category uses the same coefficients as lodgepole pine, and “other softwoods”
uses the same coefficients as Pacific silver fir. Diameter growth for red alder in the AK variant is shown
later in this section.
{4.7.1.1} Used for large trees with DBH > 10.0”
ln(DDS) = b1 + (b2 * EL) + (b3 * EL^2) + (b4 * ln(SI)) + (b5 * sin(ASP)) + (b6 * cos(ASP)) + (b7 * SL) + (b8 *
SL^2) + (b9 * ln(DBH)) + (b10 * ln(BA)) + (b11 * CR) + (b12 * CR^2) + (b13 * DBH^2) + (b14 *
BAL / (ln(DBH + 1.0))) + (b15 * BAL) + (b16 * BA) + (b17 * RELHT)
{4.7.1.2} Used for large trees with DBH < 10.0”
ln(DDS) = b1 + (b2 * EL) + (b3 * EL^2) + (b4 * ln(SI)) + (b5 * sin(ASP)) + (b6 * cos(ASP)) + (b7 * SL) + (b8 *
SL^2) + (b9 * ln(DBH)) + (b10 * ln(BA)) + (b11 * CR) + (b12 * CR^2) + (b13 * DBH^2) + (b14 *
BAL / (ln(DBH + 1.0)))
where:
DDS
EL
SI
ASP
SL
CR
DBH
BA
BAL
RELHT
b1
b2 - b17
is the predicted periodic change in squared inside-bark diameter
is stand elevation (in hundreds of feet)
is species site index
is stand aspect in radians
is stand slope expressed as a ratio (percent / 100)
is crown ratio expressed as a proportion
is tree diameter at breast height
is total stand basal area
is total basal area in trees larger than the subject tree
is the total height of the tree divided by the top height of the stand
is a location-specific coefficient shown in tables 4.7.1.2 and 4.7.1.5
are species-specific coefficients shown in tables 4.7.1.1 and 4.7.1.4
19
Table 4.7.1.1 Location class by species and location code for equation {4.7.1.1} in the AK variant.
Location Code
701 - British Columbia / Makah Indian
Reservation
1002 - Tongass National Forest: Stikine
Area
1003 - Tongass National Forest: Chatham
Area, and
1004 - Chugach National Forest
1005 - Tongass National Forest: Ketchikan
Area
Species Code
RC SF,OS MH WH YC LP,OH SS
AF
CW
4
2
4
4
1
3
3
1
4
1
2
1
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
3
2
3
3
3
3
3
3
3
1
WS
Table 4.7.1.2 b1 values by location class and species for equation {4.7.1.1} in the AK variant.
Location
Class
1
2
3
4
Species Code
WS
RC
SF, OS
MH
WH
YC
LP, OH
SS
AF
CW
-3.46832
1.10897
-3.46832
-1.86637
-2.23801
-0.79657
-0.79657
-3.14889
-3.46832
-0.107648
-3.48281
1.52503
-3.48281
-1.71679
-2.09016
-1.14325
-1.14325
-3.20919
-3.48281
0
-3.23448
0
-3.23448
-1.56184
-1.94542
-0.41948
-0.41948
-2.96203
-3.23448
0
-3.61663
0
-3.61663
-1.99657
0
0
0
0
-3.61663
0
Table 4.7.1.3 Coefficients (b2 - b17) for equation 4.7.1.1 in the AK variant.
Species Code
Coefficient
WS
RC
SF, OS
MH
b2
0.00039 -0.01052
0.00039
0.00224
b3
-0.000009 0.000104 -0.000009 -0.000009
b4
1.12514
0.00573
1.12514
0.74079
b5
-0.19185
0.0167
-0.19185 -0.10205
b6
-0.18793 0.00794
-0.18793 0.04097
b7
-1.42938 0.02871
-1.42938 -1.35921
b8
1.09399
0.03586
1.09399
1.15906
b9
0.56846
1.07184
0.56846
0.38233
b10
0
-0.44018
0
0
b11
4.60641
2.46701
4.60641
3.28729
b12
-3.33043 -1.86814
-3.33043 -2.36796
b13
-0.000165* -0.0002390 -0.000165*
0
b14
-0.02759 -0.00128
-0.02759 -0.02029
b15
0.0084
0.00198
0.0084
0.00608
b16
-0.00215
0
-0.00215 -0.00137
b17
0
0.2975
0
0
20
WH
YC
0.00438 -0.01272
-0.000019 0.000046
0.83695
0.20346
-0.07308 -0.18677
-0.03751 0.09184
-1.56867 1.27878
1.23542 -1.02205
0.62381
0.99465
-0.14942 -0.20534
3.06852
2.39021
-2.07432 -1.60504
-0.000124 -0.000003
-0.00638 -0.00646
0
0.00402
0
0
0
-0.10963
Species Code
Coefficient LP, OH
SS
AF
CW
b2
-0.01272 0.00047
0.00039 -0.075986
b3
0.000046 -0.000008 -0.000009 0.001193
b4
0.20346
1.27029
1.12514 0.227307
b5
-0.18677
-0.1379
-0.19185 -0.86398
b6
0.09184 -0.23642 -0.18793 0.085958
b7
1.27878 -0.86127 -1.42938
0
b8
-1.02205 0.54058
1.09399
0
b9
0.99465
0.68136
0.56846 0.889596
b10
-0.20534 -0.26754
0
0
b11
2.39021
3.08338
4.60641 1.732535
b12
-1.60504 -1.86516 -3.33043
0
b13
-0.000003 -0.000703 -0.000165*
0
b14
-0.00646 -0.00881 -0.02759 -0.001265
b15
0.00402
0
0.0084
0
b16
0
0
-0.00215 -0.000981
b17
-0.10963
0
0
0
*The b13 value for WS, SF, OS, or AF is –0.000042 if the location code is “1003 – Tongass National
Forest: Ketchikan Area”
Table 4.7.1.4 b1 values by location code and species for equation {4.7.1.2} in the AK variant.
Species Code
WH
SS
2.125668
1.165812
2.177696
1.165812
Location Code
701 - British Columbia / Makah Indian Reservation
1002 - Tongass National Forest: Stikine Area
1003 - Tongass National Forest: Chatham Area
1004 - Chugach National Forest
1005 - Tongass National Forest: Ketchikan Area
2.125668
2.071918
1.165812
1.32146
Table 4.7.1.5 Coefficients (B2 – B14) for equation {4.7.1.2} in the AK variant.
Coefficient
b2
b3
b4
b5
b6
b7
b8
b9
b10
Species Code
WH
SS
0.000884
0.000682
-0.000001 -0.000001
0.000972
0.001258
0.157749
0.493114
0.104729
0.024501
-1.100789 -1.817615
2.114845
4.122238
1.52525
1.780276
-0.583329 -0.595877
21
Coefficient
b11
b12
b13
b14
Species Code
WH
SS
1.50764
4.428345
0
-2.518086
-0.000792 -0.000866
-0.005402 -0.006182
Large-tree diameter growth for red alder is predicted from equations used in the PN variant identified
in equation set {4.7.1.3}. While not shown here, this diameter growth estimate is eventually converted
to the DDS scale.
{4.7.1.3} Used for red alder
trees < 18” DBH: DG = CONST - 0.166496*DBH + 0.004618*DBH^2
trees > 18” DBH: DG = CONST - (CONST/10.)*( DBH -18.)
where:
DG
CONST
DBH
BA
is tree diameter growth
is equal to: 3.250531 - 0.003029*BA
is tree diameter at breast height
is total stand basal area
4.7.2 Large Tree Height Growth
In the AK variant, equations {4.7.2.1} to {4.7.2.5} are used to estimate large tree height growth for all
species except red alder and black cottonwood.
{4.7.2.1} Used for all species except red alder and black cottonwood
POTHTG = exp[b0 + (b1 * ln(DG)) + (b2 * HT^2) + (b3 * SI) + (X90 ) + (b4 * ln(DBH)) + (b5 * ln(HT))]
{4.7.2.2} TERM1 = (1 – exp(-0.03563 * CR)^ 0.907878)
{4.7.2.3} TERM2
For western red cedar and Alaska cedar: TERM2 = 0.84875 – (0.03039 * DBH) + (0.00076 * DBH^2)
+ (0.00313 * SI)
All other species: TERM2 = 1
{4.7.2.4} MOD
40.1 < DBH <90: MOD = 3.01 – (0.06 * DBH) + (0.00033 * DBH^2)
DBH < 40.1 or DBH > 90: MOD = 1
{4.7.2.5} HTG = POTHTG * TERM1 * TERM2 * MOD
where:
POTHTG
DG
DBH
SI
is potential height growth
is diameter growth for the cycle
is tree diameter at breast height
is species site index
22
HT
X90
CR
HTG
b0 – b5
is tree height
is 0.91607, if Western hemlock X90 =0
is crown ratio expressed as a proportion
is estimated height growth for the cycle (bounded HTG < PH)
are species-specific coefficients shown in table 4.7.2.1
{4.7.2.6} PH = 4.5 + (c0 * (SI ^ c1) + c2 * ((HT – 4.5) ^ c3)) ^ (1 / c3) – (HT – 4.5)
c0 = (1 – e(-10 * d2)) * (d0 ^ (1 / d3))
c1 = d1 / d3
c2 = e ^ (-10 * d2)
c3 = 1 / d3
d3 = e1 * (SI ^ e2)
where:
PH
SI
HT
d0 – d2
e1 – e2
is potential height growth
is species site index
is total tree height
are coefficients shown in table 4.7.2.1
are coefficients shown in table 4.7.2.1
Table 4.7.2.1 Coefficients (b0 – b5 , d0 – d2 , e1 – e2 ) for height-growth equations in the AK variant.
Coefficient
b0
b1
b2
b3
b4
b5
d0
d1
d2
e1
e2
WS, RC, SF,
MH, YC, LP, SS,
AF, OH, OS
1.5163
0.1429
-0.0000604687
0.0103
0.44146
-0.3662
3.380276
0.8683028
0.01630621
2.744017
-0.2095425
Species Code
WH
2.18643
0.2059
-0.0000784117
0.0096528
0.54334
-0.35425
6.421396
0.7642128
0.01046931
3.316557
-0.2930032
RA
59.5864
0.7953
0.00194
-0.0007403
0.9198
0
0
0
0
0
0
CW
0.6192
-5.3394
240.29
3368.9
0
0
0
0
0
0
0
For red alder and black cottonwood, height increment is obtained by subtracting estimated current
height from estimated future height, then adjusting the difference according to tree’s crown ratio and
height relative to other trees in the stand (equations 4.7.2.7 – 4.7.2.11). Estimated current height (ECH)
and estimated future height (H10) are both obtained using the equations shown below. Estimated
current height is obtained using estimated tree age at the start of the projection cycle and site index.
Estimated future height is obtained using estimated tree age at the start of the projection cycle plus
23
10-years and site index. If the estimated tree age at the start of the projection cycle is greater than 200
years then POTHTG is set to 0.1 foot.
{4.7.2.7} Used for red alder
H = SI + (b0 + (b1 * SI)) * (1 – exp(b2 + (b3 * SI) * A))^b4 – (b0 + (b1 * SI)) * (1 – exp (b2 + (b3 * SI) *
20))^b4
{4.7.2.8} Used for black cottonwood
H = (Z / (b0 + (b1 / Z)) + (b2 + (b3 / Z)) * A^-1.4) + 4.5
Z = (SI – 4.5)
{4.7.2.9} POTHTG = H10 – ECH
{4.7.2.10} MOD = 1.117148*(1.0-exp(-4.26558*CR))*(exp(2.54119 * ((HT/AVH)^0.250537-1)))
{4.7.2.11} HTG = POTHTG * MOD
where:
POTHTG
SI
A
H
DG
H10
ECH
DBH
CR
AVH
b0 – b4
is estimated height growth for the cycle
is species site index
is estimated age of the tree
is estimated tree height
is diameter growth for the cycle
is estimated tree height 10 years in the future
is estimated tree height at the start of the projection period
is tree diameter at breast height
is crown ratio expressed as a percent
average height
are species-specific coefficients shown in table 4.7.2.1
Lastly for all species, the ratio of the tree’s height to diameter is checked as shown in equation
{4.7.2.12} or {4.7.2.13}. If the height-diameter ratio is too high, then the height growth is computed
using equation {4.7.2.14}.
{4.7.2.12} Used for all species except red alder and black cottonwood
MAXHT = 27.572 * (DBH + DG)^ 0.544
{4.7.2.13} For red alder and black cottonwood
MAXHT = 59.3370816 + 3.9033821* (DBH + DG)
If MAXHT < (HT + HTG), then equation {4.7.2.14} is used to reduce the height growth to a normal rate.
{4.7.2.14} HTG = MAXHT –HT
where:
MAXHT
DBH
DG
is the maximum height
is tree diameter at breast height
is diameter growth for the cycle
24
HT
HTG
is tree height
is estimated height growth for the cycle
25
5.0 Mortality Model
The AK variant uses an SDI-based mortality model as described in Section 7.3.2 of Essential FVS: A
User’s Guide to the Forest Vegetation Simulator (Dixon 2002, referred to as EFVS). This SDI-based
mortality model is comprised of two steps: 1) determining the amount of stand mortality (section
7.3.2.1 of EFVS) and 2) dispersing stand mortality to individual tree records (section7.3.2.2 of EFVS). In
determining the amount of stand mortality, the summation of individual tree background mortality
rates is used when stand density is below the minimum level for density dependent mortality (default
is 55% of maximum SDI), while stand level density-related mortality rates are used when stands are
above this minimum level.
The equation used to calculate individual tree background mortality rates for all species is shown in
equation {5.0.1}, and this is then adjusted to the length of the cycle by using a compound interest
formula as shown in equation {5.0.2}. Coefficients for these equations are shown in table 5.0.1. The
overall amount of mortality calculated for the stand is the summation of the final mortality rate (RIP)
across all live tree records.
{5.0.1} RI = [1 / (1 + exp(p0 + p1 * DBH))] * 0.5
{5.0.2} RIP = 1 – (1 – RI)^Y
where:
RI
RIP
DBH
Y
p0 and p1
is the proportion of the tree record attributed to mortality
is the final mortality rate adjusted to the length of the cycle
is tree diameter at breast height
is length of the current projection cycle in years
are species-specific coefficients shown in table 5.1.1
Table 5.0.1 Coefficients used in the background mortality equation {5.0.1} in the AK variant.
Species
Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
OS
p0
6.5112
6.5112
7.2985
5.1677
9.6943
5.1677
5.9617
9.6943
5.1677
5.5877
5.5877
5.5877
5.1677
p1
-0.0052485
-0.0052485
-0.0129121
-0.0077681
-0.0127328
-0.0077681
-0.0340128
-0.0127328
-0.0077681
-0.005348
-0.005348
-0.005348
-0.0077681
26
When stand density-related mortality is in effect, the total amount of stand mortality is determined
based on the trajectory developed from the relationship between stand SDI and the maximum SDI for
the stand. This is explained in section 7.3.2.1 of EFVS.
Once the amount of stand mortality is determined based on either the summation of background
mortality rates or density-related mortality rates, mortality is dispersed to individual tree records in
relation to a tree’s percentile in the basal area distribution of the stand (PCT) using equation {5.0.3}.
This value is then adjusted by a species-specific mortality modifier shown in equation {5.0.4}.
The mortality model makes multiple passes through the tree records multiplying a record’s trees-peracre value times the final mortality rate (MORT), accumulating the results, and reducing the trees-peracre representation until the desired mortality level has been reached. If the stand still exceeds the
basal area maximum sustainable on the site the mortality rates are proportionally adjusted to reduce
the stand to the specified basal area maximum.
{5.0.3} MR = 0.84525 – (0.01074 * PCT) + (0.0000002 * PCT^3)
{5.0.4} MORT = MR * (1 – MWT) * 0.1
where:
MR
PCT
MORT
MWT
is the proportion of the tree record attributed to mortality (bounded: 0.01 < MR < 1)
is the subject tree’s percentile in the basal area distribution of the stand
is the final mortality rate of the tree record
is a mortality weight value shown in Table 5.0.2
Table 5.0.2 MWT values for the mortality equation {5.0.4} in the AK variant.
Speci
es
Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
OS
MWT
0.5
0.1
0.3
0.3
0.1
0.3
0.7
0.3
0.1
0.5
0.9
0.5
0.7
27
6.0 Regeneration
The AK variant contains a full establishment model which is explained in section 5.4.2 of the Essential
FVS Users Guide (Dixon 2002). In short, the full establishment model automatically adds regeneration
following significant stand disturbances and adds ingrowth periodically during the simulation. For the
AK variant, automatic ingrowth is added to the simulation every 50 years, not 20 years as stated in the
Essential FVS Users Guide (Dixon 2002). Users may also input regeneration and ingrowth into
simulations manually through the establishment model keywords as explained in section 5.4.3 of the
Essential FVS Users Guide (Dixon 2002). The following description applies to how sprouting occurs and
entering regeneration and ingrowth through keywords.
The regeneration model is used to simulate stand establishment from bare ground, or to bring
seedlings and sprouts into a simulation with existing trees. Sprouts are automatically added to the
simulation following harvest or burning of known sprout species (see table 6.0.1 for sprouting species).
Table 6.0.1 Regeneration parameters by species in the AK variant.
Species
Code
WS
RC
SF
MH
WH
YC
LP
SS
AF
RA
CW
OH
OS
Sprouting
Species
No
No
No
No
No
No
No
No
No
Yes
Yes
No
No
Minimum Bud
Width (in)
0.4
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.3
0.2
0.2
0.2
0.3
Minimum Tree
Height (ft)
0.5
0.5
1.0
0.5
0.5
0.5
1.0
0.5
0.5
1.0
1.0
1.0
0.5
Maximum Tree
Height (ft)
27.0
31.0
25.0
25.0
26.0
24.0
28.0
20.0
20.0
50.0
20.0
18.0
26.0
One sprout record is created for red alder and logic rule {6.0.1} is used to determine the number of
sprout records for black cottonwood. The trees-per-acre represented by each sprout record is
determined using general sprouting probability equation {6.0.2}. See table 6.0.2 for species-specific
sprouting probabilities, number of sprout records created, and reference information.
Users wanting to modify or turn off automatic sprouting can do so with the SPROUT or NOSPROUT
keywords, respectively. Sprouts are not subject to maximum and minimum tree heights found in table
6.0.1 and do not need to be grown to the end of the cycle because estimated heights and diameters
are end of cycle values.
{6.0.1} For black cottonwood:
DSTMPi ≤ 5: NUMSPRC = 1
5 < DSTMPi ≤ 10: NUMSPRC = NINT(-1.0 + 0.4 * DSTMPi)
28
DSTMPi > 10: NUMSPRC = 3
{6.0.2} TPAs = TPAi * PS
{6.0.3} For red alder: PS = ((99.9 - 3.8462 * DSTMPi) / 100)
where:
DSTMPi
NUMSPRC
NINT
TPAs
TPAi
PS
is the diameter at breast height of the parent tree
is the number of sprout tree records
rounds the value to the nearest integer
is the trees per acre represented by each sprout record
is the trees per acre removed/killed represented by the parent tree
is a sprouting probability (see table 6.0.2)
Table 6.0.2 Sprouting algorithm parameters for sprouting species in the AK variant.
Species
Code
Sprouting
Probability
Number of
Sprout Records
RA
{6.0.3}
1
CW
0.9
{6.0.1}
Source
Harrington 1984
Uchytil 1989
Gom and Rood 2000
Steinberg 2001
Regeneration of seedlings may be specified by using PLANT or NATURAL keywords. Height of the
seedlings is estimated in two steps. First, the height is estimated when a tree is 5 years old (or the end
of the cycle – whichever comes first) by using the small-tree height growth equations found in section
4.6.1. Users may override this value by entering a height in field 6 of the PLANT or NATURAL keyword;
however the height entered in field 6 is not subject to minimum height restrictions and seedlings as
small as 0.05 feet may be established. The second step also uses the equations in section 4.6.1, which
grow the trees in height from the point five years after establishment to the end of the cycle.
Seedlings and sprouts are passed to the main FVS model at the end of the growth cycle in which
regeneration is established. Unless noted above, seedlings being passed are subject to minimum and
maximum height constraints and a minimum budwidth constraint shown in table 6.0.1. After seedling
height is estimated, diameter growth is estimated using equations described in section 4.6.2. Crown
ratios on newly established trees are estimated as described in section 4.3.1.
Regenerated trees and sprouts can be identified in the treelist output file with tree identification
numbers beginning with the letters “ES”.
29
7.0 Volume
In the AK variant, volume is calculated for three merchantability standards: total stem cubic feet,
merchantable stem cubic feet, and merchantable stem board feet (Scribner Decimal C). Volume
estimation is based on methods contained in the National Volume Estimator Library maintained by the
Forest Products Measurements group in the Forest Management Service Center (Volume Estimator
Library Equations 2009). The default merchantability standards and equation numbers for the AK
variant are shown in tables 7.0.1 – 7.0.3.
Table 7.0.1 Volume merchantability standards for the AK variant.
Merchantable Cubic Foot Volume Specifications:
Minimum DBH / Top Diameter
All location codes
Stump Height
Merchantable Board Foot Volume Specifications:
Minimum DBH / Top Diameter
All location codes
Stump Height
Hardwoods
11.0 / 8.0 inches
1.0 foot
Softwoods
9.0 / 6.0 inches
1.0 foot
Lodgepole Pine
8.0 / 6.0 inches
1.0 foot
All other species
9.0 / 6.0 inches
1.0 foot
Table 7.0.2 Volume equation defaults for each species, at specific location codes, with model name.
Common Name
white spruce
western redcedar
western redcedar
Pacific silver fir
Pacific silver fir
mountain hemlock
mountain hemlock
western hemlock
Alaska cedar
Alaska cedar
lodgepole pine
lodgepole pine
Sitka spruce
subalpine fir
subalpine fir
red alder
black cottonwood
black cottonwood
other hardwoods
other hardwoods
other softwoods
Location Code
ALL
701, 1002, 1003, 1005
1004
701, 1002, 1003, 1005
1004
701, 1002, 1003, 1005
1004
ALL
701, 1002, 1003, 1005
1004
701, 1002, 1003, 1005
1004
All
701, 1002, 1003, 1005
1004
All
701, 1002, 1003, 1005
1004
701, 1002, 1003, 1005
1004
701, 1002, 1003, 1005
Equation Number
A00DVEW094
A00F32W242
A01DEMW000
A00F32W260
A01DEMW000
A00F32W260
A01DEMW000
A00F32W260
A00F32W042
A00DVEW094
A00F32W260
A01DEMW000
A00F32W098
A00F32W260
A01DEMW000
A32CURW351
A00F32W260
A00DVEW747
A00F32W260
A16DEMW098
A00F32W260
30
Model Name
Larson Volume Equation
Flewelling Profile-32ft Log Rule
Demars Profile Model
Flewelling Profile-32ft Log Rule
Demars Profile Model
Flewelling Profile-32ft Log Rule
Demars Profile Model
Flewelling Profile-32ft Log Rule
Flewelling Profile-32ft Log Rule
Larson Volume Equation
Flewelling Profile-32ft Log Rule
Demars Profile Model
Flewelling Profile-32ft Log Rule
Flewelling Profile-32ft Log Rule
Demars Profile Model
Curtis Profile Model-32ft Log Rule
Flewelling Profile-32ft Log Rule
Larson Volume Equation
Flewelling Profile-32ft Log Rule
Demars Profile Model
Flewelling Profile-32ft Log Rule
Common Name
other softwoods
Location Code
1004
Equation Number
A16DEMW098
Model Name
Demars Profile Model
Table 7.0.3 Citations by Volume Model
Model Name
Curtis Profile
Model-32ft Log
Rule
Demars Profile
Model
Flewelling
Profile-32ft Log
Rule
Larson Volume
Equation
Citation
Curtis, Robert O, David Bruce, and Caryanne VanCoevering. 1968. Volume and
Taper Tables for Red Alder. Pacifc Northwest Forest and Range Exp. Sta. Research
Paper PNW-56.
Bruce, D., 1984. Volume estimators for Sitka spruce and western hemlock in coastal
Alaska. In Inventorying forest and other vegetation of the high latitude and high
altitude regions. SAF pub 84-11. Bethesada, MD. pp. 96-102.
Unpublished. Based on work presented by Flewelling and Raynes. 1993. Variableshape stem-profile predictions for western hemlock. Canadian Journal of Forest
Research Vol 23. Part I and Part II.
Larson, Frederic R. and Kenneth C Winterberger. 1988. Tables and Equations for
Estimating Volumes of trees in the Susitna River Basin, Alaska. Pacific Northwest
Research Station Research Note PNW-478.
31
8.0 Fire and Fuels Extension (FFE-FVS)
The Fire and Fuels Extension to the Forest Vegetation Simulator (FFE-FVS) (Reinhardt and Crookston
2003) integrates FVS with models of fire behavior, fire effects, and fuel and snag dynamics. This allows
users to simulate various management scenarios and compare their effect on potential fire hazard,
surface fuel loading, snag levels, and stored carbon over time. Users can also simulate prescribed
burns and wildfires and get estimates of the associated fire effects such as tree mortality, fuel
consumption, and smoke production, as well as see their effect on future stand characteristics. FFEFVS, like FVS, is run on individual stands, but it can be used to provide estimates of stand
characteristics such as canopy base height and canopy bulk density when needed for landscape-level
fire models.
For more information on FFE-FVS and how it is calibrated for the AK variant, refer to the updated FFEFVS model documentation (Rebain, comp. 2010) available on the FVS website.
32
9.0 Insect and Disease Extensions
FVS Insect and Disease models have been developed through the participation and contribution of
various organizations led by Forest Health Protection. The models are maintained by the Forest Health
Technology Enterprise Team (FHTET) and regional Forest Health Protection specialists. Dwarf Mistletoe
is the only I&D model available in the AK variant. The dwarf mistletoe model is available in the base
FVS variant available on the FVS website. Additional details regarding the dwarf mistletoe model may
be found in chapter 8 of the Essential FVS Users Guide (Dixon 2002); for more detailed information,
users can download the individual model guides from the FHTET website.
33
10.0 Literature Cited
Arney, J. D. 1985. A modeling strategy for the growth projection of managed stands. Canadian
Journal of Forest Research. 15(3):511-518.
Bechtold, William A. 2004. Largest-Crown-Diameter Prediction Models For 53 Species In The
Western United States. Wjaf; 19(4):245-251.
Bruce, D., 1984. Volume estimators for Sitka spruce and western hemlock in coastal Alaska. In
Inventorying forest and other vegetation of the high latitude and high altitude regions. SAF pub
84-11. Bethesada, MD. pp. 96-102.
Cole, D. M.; Stage, A. R. 1972. Estimating future diameters of lodgepole pine. Res. Pap. INT-131.
Ogden, UT: U. S. Department of Agriculture, Forest Service, Intermountain Forest and
Range Experiment Station. 20p.
Crookston, Nicholas. 2003. Internal Document on File. Moscow, ID: Data provided from region 1.
Crookston, Nicholas. 2005. Draft: Allometric Crown Width Equations for 34 Northwest United
States Tree Species Estimated Using Generalized Linear Mixed Effect Models.
Curtis, Robert O. 1967. Height-diameter and height-diameter-age equations for second-growth
Douglas-fir. Forest Science 13(4):365-375.
Curtis, Robert O, David Bruce, and Caryanne VanCoevering. 1968. Volume and Taper Tables for Red
Alder. Pacifc Northwest Forest and Range Exp. Sta. Research Paper PNW-56.
Dixon, G. E. 1985. Crown ratio modeling using stand density index and the Weibull distribution.
Internal Rep. Fort Collins, CO: U. S. Department of Agriculture, Forest Service, Forest
Management Service Center. 13p.
Dixon, Gary E. comp. 2002 (revised frequently). Essential FVS: A user’s guide to the Forest
Vegetation Simulator. Internal Rep. Fort Collins, CO: U.S. Department of Agriculture, Forest
Service, Forest Management Service Center.
Donnelly, Dennis. 1996. Internal Document On File. Fort Collins, CO: Data provided from region 6.
Farr, Wilbur A. 1984. Site index and height growth curves for unmanaged even-aged stands of
western hemlock and Sitka spruce in southeast Alaska. Res. Pap. PNW-326. Portland, OR:
UDSA Forest Service, Pacific Northwest Forest and Range Experiment Station. 26p.
Unpublished. Based on work presented by Flewelling and Raynes. 1993. Variable-shape stem-profile
predictions for western hemlock. Canadian Journal of Forest Research Vol 23. Part I and Part II.
Gom, L. A., & Rood, S. B. (2000). Fire induces clonal sprouting of riparian cottonwoods. Canadian
Journal of Botany, 77(11), 1604-1616.
Harrington, Constance A. 1984. Factors influencing initial sprouting of red alder. Canadian Journal of
Forest Research. 14: 357-361.
34
Hegyi, F.; Jelink, J.J.; Viszlai, J.; Carpenter, D.B. 1979. Site Index Equations and Curves for the
Major Tree Species in British Columbia. Forest Inv. Rep. No. 1. Ministry of Forests Victoria,
BC. November 1979, revised September 1981.
Johnson, Norman L. and Kotz, Samuel. 1970. Continuous univariate distributions-1. Boston, MA:
Houghton Mifflin company. 300 p.
Krajicek, J.; Brinkman, K.; Gingrich, S. 1961. Crown competition – a measure of density. Forest
Science. 7(1):35-42
Larson, Frederic R. and Kenneth C Winterberger. 1988. Tables and Equations for Estimating Volumes of
trees in the Susitna River Basin, Alaska. Pacific Northwest Research Station Research Note
PNW-478.
Moeur, Melinda. 1981. Crown Width And Foliage Weight Of Northern Rocky Mountain Conifers.
USDA Forest Service, Int-183.
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Vegetation Simulator: Updated Model Documentation. Internal Rep. Fort Collins, CO: U. S.
Department of Agriculture, Forest Service, Forest Management Service Center. 379 p.
Reinhardt, Elizabeth; Crookston, Nicholas L. (Technical Editors). 2003. The Fire and Fuels
Extension to the Forest Vegetation Simulator. Gen. Tech. Rep. RMRS-GTR-116. Ogden, UT:
U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 209 p.
Stage, A. R. 1973. Prognosis Model for stand development. Res. Paper INT-137. Ogden, UT: U. S.
Department of Agriculture, Forest Service, Intermountain Forest and Range Experiment
Station. 32p.
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[Online]. U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fire
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number two of the soil-site index administrative study. Juneau, AK: USDA Forest Service,
Alaska Region. 17 p.
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36
11.0 Appendices
11.1 Appendix A: Site Index Conversion Information
Site index curves and soil information from the original data sets used to build the AK variant were all
converted to Farr (1984) site curves. These conversions are below.
A) Hegyi, et al Site Curves
Hegyi, et al (1981), site curves for the major tree species in British Columbia were directly converted to
Farr (1981) curves, because the data had height and age.
B) Stephens, et al 1969
Stephens, et al (1969) base age 100 curves were converted to Farr (1984) base age 50 curves as seen in
table 11.1.1.
Table 11.1.1 Conversion of Stephens et al (1969) site index to Farr (1984).
SGB 100
150
140
130
120
110
100
90
80
70
Farr 50
100
93
85
80
75
65
60
55
45
C) Taylor, R.F. 1934
Equation {11.1.1} converts Taylor 100 to Farr 50 for western hemlock, and equation {11.1.2} converts
Taylor 100 to Farr 50 for Sitka spruce.
{11.1.1} western hemlock site index = -29.47 - 0.14392 * A + 1.58593* S - 0.0045079 * S^2
{11.1.2} Sitka spruce site index = 21.38 - 0.33969 * A + 0.68586*S + 0.0019147 * S^2
where:
S
A
=Taylor site at 100 years
=Total Age.
D) Farr 1984
These were used directly or adjusted for species by equations {11.1.3} or {11.2.4}. These relationships
were taken directly from Farr’s (1984) publication.
{11.1.3} western hemlock site index = 24.41 + 0.674 * Sitka spruce site index
{11.1.4} Sitka spruce site index = -6.62 + 1.152 * western hemlock site index
37
E) Soils Information
Use of soils information presented some special problems as different areas used different soils
classifications and the same soil in different areas might have different productivity. Estimates of Farr
site 50 for various soils series are given in table 11.1.2.
Table 11.1.2 Farr site index by soil series for southeast Alaska/coastal British Columbia.
Soil Series
Annahootz
Calamity
Edgecumbe
Farragut
Foad
Golden
Grindall
Guguak
Gunnuk
Helm
Hofstad
Hollow
Hydaburg
Isidor
Kadashan
Kaikli
Karheen
Karta
Kasiana
Kasnyku
Kina
Kogish
Kootznahoo
Kupreanof
Kushneahin
Leisnoi
Magnetic
Maybeso
McGilvery
Meares
Mitkof
Mosman
Nakwasina
Naukati
Chatham
100
Ketchikan
Stikine
10
85
85
100
10
100
60
60
80
10
70
80
10
65
55
60
50
55
55
65
10
10
55
100
10
80
80
55
100
65
100
30
20
100
100
55
90
38
10
30
20
5
50
65
90
55
80
100
90
50
60
80
Soil Series
Partofshikof
Peril
Remedios
Rynda
Salt Chuck
Sarkar
Shakan
Shelikof
Shinaku
Sitka
Sloduc
Sokolof
South Bight
South Mountain
St. Nicholas
Staney (Bog)
Sukoi
Sunnyhay
Taku
Tokeen
Tolsto
Tonowek
Traitors
Tuxekan
Ulloa
Verstovia
Vixen
Wadleigh
Waterfall
Yakobi
Yakutat
Chatham
80
80
100
Ketchikan
100
90
65
60
60
100
55
100
100
55
100
100
55
65
80
60
55
10
85
100
90
100
100
100
100
75
100
60
80
80
100
90
100
65
80
85
80
0
10
10
100
100
100
100
100
100
100
100
100
100
80
80
85
39
Stikine
100
100
80
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